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Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
25
Congruent Figures Module Quiz: Modified
1. Which best describes the sequence of the transformation given in the graph?
A Rotate ABC 90° clockwise about
the origin and then reflect across the y-axis.
B Reflect ABC over y-axis and then rotate 90° clockwise about the origin.
C Reflect ABC over y-axis and then rotate 90° counterclockwise about the origin.
For 2–3, use the figures below.
ABC XYZ≅
2. What is the side length ?XZ
A Since , .ABC XYZ BC XZ≅ ≅ BC = XZ, and BC = 15 in., so XZ = 15 in.
B Since .ABC XYZ, AC XZ≅ ≅ AC = XZ, and AC = 15 in., so XZ = 15 in.
C Since , .ABC XYZ AC XZ≅ ≅ AC = XZ, and AC = 11 in., so XZ = 11 in.
3. What is the measure of ?C∠ A 31° B 57° C 92°
For 4–5, use the figures below.
ABCD ≅ MNOP 4. Which transformation can be used to map
ABCD to MNOP? A rotation 270° clockwise B reflection across the x-axis C reflection across the y-axis
5. What is the coordinate notation for the transformation used? A (x, y) → (−x, y) B (x, y) → (−x, −y) C (x, y) → (−y, x)
6. Which coordinate notation describes the
transformation in the graph above?
A (x, y) → 1 1,2 2
x y⎛ ⎞⎜ ⎟⎝ ⎠
→ (x − 3, y + 2)
B (x, y) → (2x, 2y) → (x + 3, y − 2)
C (x, y) → 1 1,2 2
x y⎛ ⎞⎜ ⎟⎝ ⎠
→ (x + 3, y − 2)
MODULE
3
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
26
Congruent Figures Module Quiz: Modified
For 7–9, use the figures below.
Quadrilateral ABCD ≅ WXYZ
7. What is the length of ?YZ
________________________________________
8. What is the m ?B∠
________________________________________
9a. What is the m ?x∠
________________________________________
9b. Explain your reasoning.
________________________________________
10. KLM is reflected across the y-axis, translated along vector ⟨4, 3⟩, and then dilated which is mapped
(x, y) → 1 1
, .2 2
x y⎛ ⎞⎜ ⎟⎝ ⎠
Graph all of the
transformations.
11. What is the coordinate notation for the transformation shown?
12. RST is the image of NLM under a
series of transformations. Could each of these possible series be used to find the image RST from the preimage
?NLM
a. Reflect RST across y-axis and
then translate along the vector ⟨−2, −4⟩.
____________________________________
b. Reflect RST across x-axis and then rotate counterclockwise 270°.
____________________________________
c. Translate RST along the vector ⟨2, 4⟩, then reflect across the y-axis.
____________________________________
MODULE
3
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
118
Lines, Angles, and Triangles Unit Test: B
Use the figure for 1–2.
1. Name all angles congruent to ∠1.
________________________________________
________________________________________
2. Name all angles supplementary to ∠3.
________________________________________
________________________________________
3. Write an equation for the line that passes through (2, −5) and is parallel to 3x + 4y = 8.
________________________________________
4. For the triangles shown, state the additional congruency statement needed to prove BCD QRS≅ for the given theorem.
a. SAS Theorem
____________________________________
b. ASA Theorem
____________________________________
5. Write an equation for the line that passes through (10, 0) and is perpendicular to 3x − y = 7.
________________________________________
For 6–7, use the figure.
6. What is the sum of the interior angles of
this polygon?
________________________________________
7. Using only the sum found above, is it possible to determine the measure of each angle in the figure? Explain why or why not.
________________________________________
________________________________________
For 8–9, use the figure.
8. If m 1 53 ,∠ = ° what is m 3?∠
________________________________________
9. Derrick states that DEF is an isosceles triangle. Is Derrick correct? Explain.
________________________________________
________________________________________
10. Can a triangle have side lengths 5, 8, and 13? Explain why or why not.
________________________________________
UNIT
2
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
119
Lines, Angles, and Triangles Unit Test: B
For 11–12, use the figure.
11. If DE = 6x, what is the perimeter of the triangle in terms of x?
________________________________________
12. Can you determine m D∠ with only the information shown? If so, state the measure. If not, explain why not.
________________________________________
________________________________________
________________________________________
13. The sides of a triangle measure 8 meters and 12 meters. What are the possible side lengths for the third side? Show your work.
________________________________________
________________________________________
________________________________________
14. Which points of concurrency must lie inside a triangle? Explain.
________________________________________
________________________________________
________________________________________
For 15–16, use the figure. BCD is shown.
15. Explain how to determine the centroid for
.BCD
________________________________________
________________________________________
16. Where is the centroid for BCD located?
________________________________________
Use the figure for 17–19. Fill in blanks for the paragraph proof.
Given: ∠ ≅ ∠ ,A C BE BD≅
Prove: BA BC≅ 17. It is given that A C∠ ≅ ∠ and .BE BD≅ It
is true that B B∠ ≅ ∠ because
_______________________________________ .
18. Therefore, Δ ≅ ΔBDA BEC by the
_______________________________________ .
19. Thus, BA BC≅ because
_______________________________________ .
UNIT
2
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
30
Response to Intervention Post-Test: Congruent Figures
Use the figures for 1–3.
1. List the corresponding angles.
________________________________________
2. List the corresponding sides.
________________________________________
3. Write a congruence statement for the triangles.
________________________________________
For 4–5, use .JKM PQR≅
4. If m∠P = 86° and m∠R = 21°, what is m∠J?
________________________________________
5. If JM = 14 inches and MK = 25 inches, what is the length of RQ?
________________________________________
6. The following congruence statement represents the corresponding parts of two congruent triangles.
BCD RST≅
Choose True or False for each statement.
A BC ST≅ True False
B CB SR≅ True False C C S∠ ≅ ∠ True False D DBC TRS≅ True False
Use the following information for 7–9. The trapezoids below are congruent.
7. What is the length of ?SP
________________________________________
8. Which angle is congruent to ∠B?
________________________________________
9. Which side is longer, QR or RS?
________________________________________
For 10–13, use the figure and the congruence statement .JKM PQR≅
10. What is the measure of ∠Q?
________________________________________
11. What is the measure of ∠M?
________________________________________
12. What is the length of PQ?
________________________________________
13. If the perimeter of triangle PQR is 20 centimeters, what is the perimeter of triangle JKM?
________________________________________
SKILL
7
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
36
Response to Intervention Post-Test: Parallelograms
Use the figure for 1–3.
1. List the congruent sides.
________________________________________
2. List the congruent angles.
________________________________________
3. Name two consecutive angle pairs that include ∠C.
________________________________________ Use parallelogram PQRS for 4–5.
4. If m∠P = 2x°, m∠R = 62°, find the value for x.
________________________________________
5. If QR = 16 feet and PS = 3y − 5 feet, find the value for y.
________________________________________
6. Find the unknown angle measures.
________________________________________
7. In parallelogram RSTU, RS || TU and ST || UR . If ST = 9 inches and TU = 4 inches, find RS and UR.
________________________________________
Use parallelogram JKLM for 8–9.
8. What is the value of x?
________________________________________
9. What are the measures of all of the interior angles of the parallelogram?
________________________________________
Use the following information for 10–13. In parallelogram CDEF, AE = 3x + 4, EC = 2x + 8, BE = 4y + 1, and BD = 18.
10. What are the values of x and y?
________________________________________
11. What is the length of ?EC
________________________________________
12. What is the length of ?AC
________________________________________
13. What is the length of ?ED
________________________________________
SKILL
13
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
28
Response to Intervention Post-Test: Area of Composite Figures
Use the figure for 1–5.
1. What two shapes make up the figure?
________________________________
2. What is the length of the base of the triangle?
________________________________
3. Find the area of the triangle.
________________________________
4. Find the area of the rectangle.
________________________________
5. What is the total area of the figure?
________________________________
Use the following information for 6–9.
The shaded area represents a square picture frame with a side length of 8 inches. The width of the frame is 2 inches.
6. What is the length of the side of the unshaded square?
________________________________
7. Find the area of the unshaded square.
_________________________________
8. Find the area of the large square.
_________________________________
9. What is the area of the frame represented by the shaded region?
_________________________________
Use the following information for 10–14. Use 3.14 for π. Round answers to the nearest hundredth, if necessary. A window is composed of a rectangle and a semicircle. The height of the window is 7 feet and the width is 4 feet.
10. What is the radius of the semicircle?
_________________________________
11. Find the area of the semicircle.
_________________________________
12. What is the height of the window without the top semicircle?
_________________________________
13. Find the area of the rectangle.
_________________________________
14. What is the total area of the window?
________________________________________
SKILL
5
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
32
Response to Intervention Post-Test: Distance and Midpoint Formulas
Use the figure for 1–4.
1. What is the midpoint of AB?
________________________________________
2. What is the midpoint of CD?
________________________________________
3. What is the midpoint of EF?
________________________________________
4. What is the midpoint of GH?
________________________________________
5. A segment has coordinates (−4, 9) and (0, 7). What is the midpoint of the segment?
________________________________________
6. A segment has coordinates (8, −5) and (8, 4). What is the midpoint of the segment?
________________________________________
7. A segment ST is graphed on a coordinate plane. The endpoint S is at (−3, 2). The midpoint is at (−3, −2). What are the coordinates of the other endpoint T?
________________________________________
________________________________________
Use the following information for 8–10. A map is drawn on a coordinate grid.
Each unit is equal to 1 mile.
8. David would like to meet a friend at the halfway point between his home and the library. What is the location of the midpoint between David’s home and the library?
________________________________________
9. What is the distance between the park and the library?
________________________________________
________________________________________
10. What is the distance between David’s home and the park?
________________________________________
________________________________________
11. A segment measures 10 units. One end of the segment has an endpoint at (3, −6). What is another possible endpoint to this segment?
________________________________________
SKILL
9
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
44
Response to Intervention Post-Test: Rate of Change and Slope
1. What is the rate of change in the table?
x y
0 0
4 2
8 4
12 6
________________________________________
2. The rate of change for a growing tree is 3 feet every 2 years. What is the unit rate?
________________________________________
Use the graph for 3–6. Calculate the slope for each line.
3. What is the slope of ?AB
________________________________________
4. What is the slope of ?CD
________________________________________
5. What is the slope of ?EF
________________________________________
6. What is the slope of ?GH
________________________________________
7. What is the slope of the line that passes through points (−2, 5) and (6, 10)?
________________________________________
________________________________________
________________________________________
8. What is the slope of the line that passes through points (3, 6) and (−8, 2)?
________________________________________
________________________________________
________________________________________
9. What is the slope of the line that passes through points (9, 0) and (9, −3)?
________________________________________
________________________________________
________________________________________
10. Tell whether each statement is true or false. A Vertical lines have undefined slopes. True False B Slopes must be either positive or
negative. True False C A line with slope −3 goes up from left
to right. True False D If a line has the same y-coordinates,
the slope must be zero. True False
E The slopes 12− and 1
2− are
equivalent. True False
SKILL
21
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
49
Response to Intervention Post-Test: Using Slope and y-intercept
For 1–2, use the graph.
1. Find the slope of the line.
________________________________________
2. What is the y-intercept?
________________________________________
3. Write an equation in slope-intercept form for the given slope and y-intercept.
slope: 5; y-intercept: 15
−
________________________________________
4. Find the slope and y-intercept for the graph of the equation y = −x + 4
________________________________________
________________________________________
5. The graph of the following equation has a
slope of 32
. Choose True or False for
each equation.
A y = x + 32
True False
B y = 32
x + 1 True False
C 2x + 3y = 12 True False D −3x + 2y = 4 True False
6. Write the equation 4x + 2y = 6 in slope-intercept form.
________________________________________
7. Find the slope and y-intercept for the graph of the equation −2x + 3y = 1.
________________________________________
________________________________________
8. Graph the equation y = − 34
x + 1.
For 9–10, use the following information.
An amusement park charges $15 per ticket for admission and $5 for parking. The equation y = 15x + 5 represents the total cost y for x tickets. 9. What is the slope of the line? Describe its
meaning.
________________________________________
________________________________________
10. What is the y-intercept? Describe its meaning.
________________________________________
________________________________________
SKILL
26
Name ________________________________________ Date __________________ Class __________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
51
Response to Intervention Post-Test: Writing Equations of Parallel, Perpendicular, Vertical, and Horizontal Lines
1. State whether the following sets of lines are parallel, perpendicular, or neither. A y = 5 and y = −2
____________________________________
B y = 8 and x = 8
____________________________________
C y = 4x + 8 and y = −4x − 2
____________________________________
D y = −x + 6 and y = x + 1
____________________________________
E y = 6x + 2 and y = 6x
____________________________________
2. What is an equation for the line parallel to y = 2 going through the point (7, −4)?
________________________________________
________________________________________
3. What is an equation for the line parallel to y = 2x + 4 going through the point (1, 1)?
________________________________________
________________________________________
4. What is an equation for the line perpendicular to y = 5x − 1 going through the point (−2, −4)?
________________________________________
________________________________________
5. What is an equation for the line parallel to y = −x + 2 going through the point (−3, −5)?
________________________________________
________________________________________
6. What is an equation for the line perpendicular to x = −1 going through the point (−2, −3)?
________________________________________
________________________________________
7. What is an equation for the line parallel to x = 0 going through the point (6, 5)?
________________________________________
________________________________________
8. What is an equation for the line
perpendicular to 1 13
y x= + going
through the point (−2, 3)?
________________________________________
________________________________________
9. Tell whether each statement is true or false. A Perpendicular lines have opposite
slopes. True False
B The negative reciprocal of 4 is 14
−
True False C Lines that are parallel have the same
slope. True False D Horizontal lines are always
perpendicular. True False E Vertical lines are always parallel. True False F Lines with the same slope are always
parallel. True False G Horizontal and vertical lines are
always perpendicular. True False
SKILL
28